PYQ Vault

MHT-CET 2025 (22 April Shift II), Paper I, Mathematics question paper

50 questions · 100 marks · 90 minutes · +2 per correct answer, no negative marking

Every question in the order it was set, free to read. Tap an option to check it, or open the answer and worked solution. Answers open as you go; sign in free to keep opening them.

Sit it as a timed mock
  1. 1
    Considering only the principal values of the inverse trigonometric function, the value of tan⁡(cos⁡−1152−sin⁡−1417)\tan\left( \cos^{- 1}\frac{1}{5\sqrt{2}}-\sin^{- 1}\frac{4}{\sqrt{17}} \right) is

    Tap an option to check your answer.

  2. 2
    The line L is passing through (1,2,3)(1,2,3). The distance of any point on the line L from the line r‾=(3λ−1)i^+(−2λ+3)j^+(4+λ)k^\overline{r}= (3\lambda - 1)\widehat{i}+ ( - 2\lambda + 3)\widehat{j}+ (4 + \lambda)\widehat{k} is constant. Then the line L does not pass through the point

    Tap an option to check your answer.

  3. 3
    The distance of the plane r‾=(i^−j^)+λ(i^+j^+k^)+μ(i^−2j^+3k^)\overline{r}= (\widehat{i}-\widehat{j}) + \lambda(\widehat{i}+\widehat{j}+\widehat{k}) + \mu(\widehat{i}- 2\widehat{j}+ 3\widehat{k}) from the origin is

    Tap an option to check your answer.

  4. 4
    If the angle between the line x=y−12=z−3λx =\frac{y - 1}{2}=\frac{z - 3}{\lambda} and the plane x+2y+3z=4x + 2y + 3z = 4 is cos⁡−1514\cos^{- 1}\sqrt{\frac{5}{14}}, then the value of λ\lambda is

    Tap an option to check your answer.

  5. 5
    If f(1)=3,f′(1)=2f(1) = 3,f^{'}(1) = 2, then ddx{log⁡[f(ex+2x)]}\frac{d}{dx}\left\{ \log\left\lbrack f\left( e^{x}+ 2x \right) \right\rbrack \right\} at x=0x = 0 is

    Tap an option to check your answer.

  6. 6
    If 16sin⁡θ,cos⁡θ,tan⁡θ\frac{1}{6}\sin\theta,\cos\theta,\tan\theta are in G.P., then the general solution of θ\theta is

    Tap an option to check your answer.

  7. 7
    Let f be a function which is continuous and differentiable for all xx. If f(1)=1f(1) = 1 and f′(x)≤5f^{'}(x) \leq 5 for all xx in [1,5]\lbrack 1,5\rbrack, then the maximum value of f (5) is

    Tap an option to check your answer.

  8. 8
    In a triangle ABC with usual notations if, cot⁡A2=b+ca\cot\frac{A}{2}=\frac{b + c}{a}, then the triangle ABCABC is

    Tap an option to check your answer.

  9. 9
    If matrix A=111[−17−242a42−315]A =\frac{1}{11}\begin{bmatrix} - 1 & 7 & - 24 \\ 2 & a & 4 \\ 2 & - 3 & 15 \end{bmatrix} and A−1=[3342−34b−1c]A^{- 1}=\begin{bmatrix} 3 & 3 & 4 \\ 2 & - 3 & 4 \\ b & - 1 & c \end{bmatrix}, then the values of a,b,ca,b,c respectively are ____\_\_\_\_

    Tap an option to check your answer.

  10. 10
    pp : If 7 is an odd number then 7 is divisible by 2. q : If 7 is prime number then 7 is an odd number. If V1V_{1} and V2V_{2} are respective truth values of contrapositive of pp and qq then (V1,V2)≡\left( V_{1},V_{2} \right)\equiv

    Tap an option to check your answer.

  11. 11
    lim⁡x→1(log⁡33x)log⁡x8=\lim_{x \rightarrow 1} \left( \log_{3}3x \right)^{\log_{x}8}=... .

    Tap an option to check your answer.

  12. 12
    The function f(x)=sin⁡4x+cos⁡4xf(x) =\sin^{4}x +\cos^{4}x increases if

    Tap an option to check your answer.

  13. 13
    The values of bb and cc for which the identity f(x+1)−f(x)=8x+3f(x + 1) - f(x) = 8x + 3 is satisfied, where f(x)=bx2+cx+df(x) = bx^{2}+ cx + d, are

    Tap an option to check your answer.

  14. 14
    ∫x3x4+5x2+4 dx=\int\frac{x^{3}}{x^{4}+ 5x^{2}+ 4}\text{ }dx =

    Tap an option to check your answer.

  15. 15
    z=3+2isinθ1−2isinθ,(i=−1)z =\frac{3 + 2isin\theta}{1 - 2isin\theta},(i =\sqrt{- 1}) will be purely imaginary if θ=\theta =

    Tap an option to check your answer.

  16. 16
    The equations of the tangents to the circle x2+y2=36x^{2}+y^{2}= 36 which are perpendicular to the line 5x+y=25x + y = 2, are

    Tap an option to check your answer.

  17. 17
    If sin⁡A=nsin(A+2 B)\sin A = nsin(A + 2\text{ }B), then tan⁡(A+B)=\tan(A + B) =

    Tap an option to check your answer.

  18. 18
    The number of integral values of pp for which the vectors (p+1)i^−3j^+pk^,pi^+(p+1)j^−3k^(p + 1)\widehat{i}- 3\widehat{j}+ p\widehat{k},p\widehat{i}+ (p + 1)\widehat{j}- 3\widehat{k} and −3i^+pj^+(p+1)k^- 3\widehat{i}+ p\widehat{j}+ (p + 1)\widehat{k} are linearly dependent vectors, are

    Tap an option to check your answer.

  19. 19
    ∫0π4(tan⁡x+cot⁡x)dx=\int_{0}^{\frac{\pi}{4}} (\sqrt{\tan x}+\sqrt{\cot x})dx =

    Tap an option to check your answer.

  20. 20
    If a curve y=ax+bxy = a\sqrt{x}+ bx passes through the point (1,2)(1,2) and the area bounded by this curve, line x=4x = 4 and the X -axis is 8 sq. units, then the value of a−ba - b is

    Tap an option to check your answer.

  21. 21
    The foci of a hyperbola coincide with the foci of the ellipse x225+y29=1\frac{x^{2}}{25}+\frac{y^{2}}{9}= 1. The equation of the hyperbola with eccentricity 2 is

    Tap an option to check your answer.

  22. 22
    The differential equation satisfied by y=Xsin (6t+5)+Ycos(6t+5)y = Xsin\ (6t + 5) + Ycos(6t + 5) is (where X and Y are constants)

    Tap an option to check your answer.

  23. 23
    A wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet, hung in the open air, loses half its moisture during the first hour, then 90%90\% of the moisture will be lost in ____\_\_\_\_ hours.

    Tap an option to check your answer.

  24. 24
    If a random variable XX has p.d.f. f(x)={ax22+bx, if 1≤x≤30, otherwisef(x)=\begin{cases}\dfrac{ax^{2}}{2}+bx & ,\text{ if }1\le x\le 3\\ 0 & ,\text{ otherwise}\end{cases} and f(2)=2f(2)=2, then the values of aa and bb are, respectively

    Tap an option to check your answer.

  25. 25
    If pˉ=2i^+k^,qˉ=i^+j^+k^,rˉ=4i^−3j^+7k^\bar{p}= 2\widehat{i}+\widehat{k},\bar{q}=\widehat{i}+\widehat{j}+\widehat{k},\bar{r}= 4\widehat{i}- 3\widehat{j}+ 7\widehat{k} and a vector m‾\overline{m} is such that m‾×q‾=r‾×q‾,m‾⋅p‾=0\overline{m}\times\overline{q}=\overline{r}\times\overline{q},\overline{m}\cdot\overline{p}= 0, then m‾=\overline{m}=... .

    Tap an option to check your answer.

  26. 26
    If the point (1,α,β)(1,\alpha,\beta) lies on the line of the shortest distance between the lines x+2−3=y−24=z−52\frac{x + 2}{- 3}=\frac{y - 2}{4}=\frac{z - 5}{2} and x+2−1=y+62,z=1\frac{x + 2}{- 1}=\frac{y + 6}{2},z = 1, then α+β=\alpha + \beta =

    Tap an option to check your answer.

  27. 27
    The angle between the lines x−3y−4=0,4y−z+5=0x - 3y - 4 = 0,4y - z + 5 = 0 and x+3y−11=0,2y−z+6=0x + 3y - 11 = 0,2y - z + 6 = 0 is

    Tap an option to check your answer.

  28. 28
    If the area of parallelogram, whose diagonals are i^−j^+2k^\widehat{i}-\widehat{j}+ 2\widehat{k} and 2i^+3j^+αk^2\widehat{i}+ 3\widehat{j}+ \alpha\widehat{k} is 932\frac{\sqrt{93}}{2} sq. units, then α=\alpha =

    Tap an option to check your answer.

  29. 29
    The correct constraints for the given feasible region are ....

    Tap an option to check your answer.

  30. 30
    The circumradius of the triangle formed by the lines xy+2x+2y+4=0xy + 2x + 2y + 4 = 0 and x+y+2=0x + y + 2 = 0 is

    Tap an option to check your answer.

  31. 31
    Derivative of x(xx)x^{\left( x^{x} \right)} is

    Tap an option to check your answer.

  32. 32
    The number of solutions of tan⁡−1(x+2x)−tan⁡−1(4x)−tan⁡−1(x−2x)=0\tan^{- 1}\left( x+\frac{2}{x} \right)-\tan^{- 1}\left( \frac{4}{x} \right)-\tan^{- 1}\left( x-\frac{2}{x} \right)= 0 are

    Tap an option to check your answer.

  33. 33
    The derivative of tan⁡−1(1+x2−1x)\tan^{- 1}\left( \frac{\sqrt{1 +x^{2}}- 1}{x} \right) w.r.t. tan⁡−1(2x1−x21−2x2)\tan^{- 1}\left( \frac{2x\sqrt{1 -x^{2}}}{1 - 2x^{2}} \right) at x=0x= 0 is

    Tap an option to check your answer.

  34. 34
    The normal to the curve x=9(1+cos⁡θ)x= 9(1 +\cos\theta), y=9sin⁡θy= 9\sin\theta at θ\theta always passes through the fixed point

    Tap an option to check your answer.

  35. 35
    In a triangle ABC with usual notations, if 3a=b+c3a = b + c, then cot⁡B2⋅cot⁡C2=\cot\frac{B}{2}\cdot \cot\frac{C}{2}=

    Tap an option to check your answer.

  36. 36
    If p : switch S1S_{1} is closed, q: switch S2S_{2} is closed, r : switch S3S_{3} closed, then the symbolic form of the following switching circuit is equivalent to Switching Circuit:

    Tap an option to check your answer.

  37. 37
    If f(x)={1−cos⁡4xx2,x<0a,x=0x(16+x)1/2−4,x>0f(x)=\begin{cases}\dfrac{1-\cos4x}{x^2}, & x<0\\ a, & x=0\\ \dfrac{\sqrt{x}}{(16+\sqrt{x})^{1/2}-4}, & x>0\end{cases} is continuous at x=0x=0, then a=a=

    Tap an option to check your answer.

  38. 38
    ∫sec⁡23x⋅csc⁡⁡43x dx=\int\sec^{\frac{2}{3}}x\cdot\operatorname{\csc}^{\frac{4}{3}}x\,dx=

    Tap an option to check your answer.

  39. 39
    If the lengths of three vectors aˉ,bˉ\bar{a},\bar{b} and cˉ\bar{c} are 5,12,135,12,13 units respectively, and each one is perpendicular to the sum of the other two, then ∣a‾+b‾+c‾∣=|\overline{a}+\overline{b}+\overline{c}| =

    Tap an option to check your answer.

  40. 40
    An open tank with a square bottom is to contain 4000 cubic cm. of liquid. The dimensions of the tank so that the surface area of the tank is minimum, is

    Tap an option to check your answer.

  41. 41
    If four digit numbers are formed by using the digits 1,2,3,4,5,6,71,2,3,4,5,6,7 without repetition, then out of these numbers, the numbers exactly divisible by 25 are

    Tap an option to check your answer.

  42. 42
    ∫e2x(sin⁡2x cos⁡2x−1)sin⁡22x dx=\int e^{2x}\dfrac{(\sin2x\,\cos2x-1)}{\sin^{2}2x}\,dx=

    Tap an option to check your answer.

  43. 43
    Three urns respectively contain 2 white and 3 black, 3 white and 2 black and 1 white and 4 black balls. If one ball is drawn from each urn, then the probability that the selection contains 1 black and 2 white balls is

    Tap an option to check your answer.

  44. 44
    The lines x+2ay+a=0,x+3by+b=0x + 2ay + a = 0,x + 3by + b = 0, x+4cy+c=0x + 4cy + c = 0 are concurrent then a,b,ca,b,c are in

    Tap an option to check your answer.

  45. 45
    In a box containing 100 apples, 10 are defective. The probability that in a sample of 6 apples, 3 are defective is

    Tap an option to check your answer.

  46. 46
    The value of the integral ∫12xdx(x+2)(x+3)\int_{1}^{2} \frac{xdx}{(x + 2)(x + 3)} is

    Tap an option to check your answer.

  47. 47
    The general solution of the differential equation dy dx+sin⁡(x+y2)=sin⁡(x−y2)\frac{dy}{\text{ }dx}+ \sin\left( \frac{x + y}{2} \right)= \sin\left( \frac{x - y}{2} \right) is

    Tap an option to check your answer.

  48. 48
    Four defective oranges are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. The probability distribution of defective oranges is

    Tap an option to check your answer.

  49. 49
    The equation of the curve passing through (2,92)\left( 2,\frac{9}{2} \right) and having the slope (1−1x2)\left( 1 -\frac{1}{x^{2}} \right) at (x,y)(x,y) is

    Tap an option to check your answer.

  50. 50
    The projection of the line segment joining P(2,−1,0)P(2, - 1,0) and Q(3,2,−1)Q(3,2, - 1) on the line whose direction ratios are 1,2,21,2,2 is

    Tap an option to check your answer.

Want the real exam feel? Sit this paper with a 90-minute timer and get your score straight away.

Sit it as a timed mock